Rights statement: This is the author’s version of a work that was accepted for publication in International Journal of Solids and Structures. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in International Journal of Solids and Structures, 234-235, 2022 DOI: 10.1016/j.ijsolstr.2021.111238
Accepted author manuscript, 1.4 MB, PDF document
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Final published version
Research output: Contribution to Journal/Magazine › Journal article › peer-review
Research output: Contribution to Journal/Magazine › Journal article › peer-review
}
TY - JOUR
T1 - States of self-stress in symmetric frameworks and applications
AU - Schulze, Bernd
AU - Miller, Cameron
AU - Mazurek, Arek
AU - Baker, William
N1 - This is the author’s version of a work that was accepted for publication in International Journal of Solids and Structures. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in International Journal of Solids and Structures, 234-235, 2022 DOI: 10.1016/j.ijsolstr.2021.111238
PY - 2022/1/31
Y1 - 2022/1/31
N2 - We use the symmetry-extended Maxwell rule established by Fowler and Guest to detect states of self-stress in symmetric planar frameworks. The dimension of the space of self-stresses that are detectable in this way may be expressed in terms of the number of joints and bars that are unshifted by various symmetry operations of the framework. Therefore, this method provides an efficient tool to construct symmetric frameworks with many ‘fully-symmetric’ states of self-stress, or with ‘anti-symmetric’ states of self-stress. Maximising the number of independent self-stresses of a planar framework, as well as understanding their symmetry properties, has important practical applications, for example in the design and construction of gridshells. We show the usefulness of our method by applying it to some practical examples.
AB - We use the symmetry-extended Maxwell rule established by Fowler and Guest to detect states of self-stress in symmetric planar frameworks. The dimension of the space of self-stresses that are detectable in this way may be expressed in terms of the number of joints and bars that are unshifted by various symmetry operations of the framework. Therefore, this method provides an efficient tool to construct symmetric frameworks with many ‘fully-symmetric’ states of self-stress, or with ‘anti-symmetric’ states of self-stress. Maximising the number of independent self-stresses of a planar framework, as well as understanding their symmetry properties, has important practical applications, for example in the design and construction of gridshells. We show the usefulness of our method by applying it to some practical examples.
KW - Symmetry
KW - Rigidity
KW - Bar-joint framework
KW - Equilibrium stress
KW - Gridshell structure
U2 - 10.1016/j.ijsolstr.2021.111238
DO - 10.1016/j.ijsolstr.2021.111238
M3 - Journal article
VL - 234-235
JO - International Journal of Solids and Structures
JF - International Journal of Solids and Structures
SN - 0020-7683
M1 - 111238
ER -